Parameter Estimation of Uncertain Moving Average Model Based on Least Squares Principle

The uncertain moving average model is a powerful tool to study the time series in which the data are affected by the previous disturbance terms under uncertain environments. However, the influence of uncertain disturbance terms is often ignored in the relevant statistical inference studies. In order to solve this problem, this paper constructs a symmetric statistical invariant, normal uncertain variable, by sorting out the uncertain moving average model and combining the uncertain disturbance terms, and then applies the least square principle to the parameter estimation of the symmetric statistical invariant to determine the unknown parameters and uncertain disturbance terms in the uncertain moving average model. In addition, a numerical algorithm is designed to calculate the corresponding estimators, and the problems related to hypothesis testing and forecast are also studied. Finally, a numerical example is given to illustrate the proposed method.